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Wiktionary
local variable

n. (context programming English) A variable that has local scope; accessible only in a limited part of a program, such as a single function.

Wikipedia
Local variable

In computer science, a local variable is a variable that is given local scope. Local variable references in the function or block in which it is declared override the same variable name in the larger scope. In programming languages with only two levels of visibility, local variables are contrasted with global variables. On the other hand, many ALGOL-derived languages allow any number of nested levels of visibility, with private variables, functions, constants and types hidden within them, either by nested blocks or nested functions. Local variables are fundamental to procedural programming, and more generally modular programming: variables of local scope are used to avoid issues with side-effects that can occur with global variables.

Local variables may have a lexical or dynamic scope, though lexical (static) scoping is far more common. In lexical scoping (or lexical scope; also called static scoping or static scope), if a variable name's scope is a certain block, then its scope is the program text of the block definition: within that block's text, the variable name exists, and is bound to the variable's value, but outside that block's text, the variable name does not exist. By contrast, in dynamic scoping (or dynamic scope), if a variable name's scope is a certain block, then its scope is that block and all functions transitively called by that block (except when overridden again by another declaration); after the block ends, the variable name does not exist. Some languages, like Perl and Common Lisp, allow the programmer to choose static or dynamic scoping when defining or redefining a variable. Examples of languages that use dynamic scoping include Logo, Emacs lisp, and the shell languages bash, dash, and the MirBSD Korn shell (mksh)'s "local" declaration. Most other languages provide lexically scoped local variables.

In most languages, local variables are automatic variables stored on the call stack directly. This means that when a recursive function calls itself, local variables in each instance of the function are given distinct addresses. Hence variables of this scope can be declared, written to, and read, without any risk of side-effects to functions outside of the block in which they are declared.

Programming languages that employ call by value semantics provide a called subroutine with its own local copy of the arguments passed to it. In most languages, these local parameters are treated the same as other local variables within the subroutine. In contrast, call by reference and call by name semantics allow the parameters to act as aliases of the values passed as arguments, allowing the subroutine to modify variables outside its own scope.